We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

This text is a classic of Lenin - his essay explores materialism and its relation to capitalism and how Communism can get over this psychological wish for material and empirical ownership.

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

O que aqui se pretende é analisar a forma voltairiana de relacionar arte e política presente em sua obra, apontando seus alcances e limites a partir da noção da relação entre arte e política em Jacques Rancière. Para tal, este trabalho se divide em três momentos: no primeiro, expor a proposta voltairiana de relacionar arte e política; em seguida, entender como essa relação se dá a partir de categorias de Rancière – “partilha do sensível”, “estética da política”, “política”, “polícia”, “dissenso” (...) etc – e, por fim, aplicar essas categorias à proposta de Voltaire de relacionar arte e política com o fim de verificar se sua obra efetiva a relação almejada. (shrink)

“Toy worlds” involving actions, such as the blocks world and the Missionaries and Cannibals puzzle, are often used by researchers in the areas of commonsense reasoning and planning to illustrate and test their ideas. We would like to create a database of generalpurpose knowledge about actions that encodes common features of many action domains of this kind, in the same way as abstract algebra and topology represent common features of specific number systems. This paper is a report on the first (...) stage of this project—the design of an action description language in which this database will be written. The new language is an extension of the action language C+. Its main distinctive feature is the possibility of referring to other action descriptions in the definition of a new action domain. (shrink)

L’article aborde le sujet souvent débattu du rapport entre le détermi­nisme stoïcien et la morale pour rouvrir la question de la notion d’assentiment. Dans ce but, il réexamine les sources pour montrer deux choses : que les inter­prétations dites compatibilistes ont raison dans leur effort général pour montrer que les stoïciens restent déterministes quand ils présentent leur psychologie de l’action et défendent l’idée de responsabilité, mais qu’en même temps elles vont trop loin quand elles affirment – dans un effort de (...) systématisation de la stratégie stoïcienne – que l’assentiment est le simple effet de la rencontre du caractère particulier de l’agent et de l’impression sensorielle. En essayant de restituer l’ac­cent que les stoïciens ont mis sur l’assentiment, l’article indique que c’est égale­ment là que réside l’ambigüité de leur psychologie de l’action, qui a contribué au paradoxe dans l’interprétation du stoïcisme : ce dernier a été dès l’origine, d’un côté, une inspiration pour ceux qui ont voulu argumenter en faveur de la liberté de l’action humaine, et de l’autre, le sujet de la critique pour la réfutation de la liberté de l’action. Dans son ensemble l’interprétation proposée est négative dans le sens où elle veut montrer comment ne pas comprendre l’assentiment, pour ouvrir la possibilité de l’examiner de nouveau, ce qui pourrait montrer enfin que l’ambigüité mentionnée est par conséquent l’expression du plus grand potentiel philosophique de la conception stoïcienne de la raison. (shrink)

The first collective monograph on one of Plato’s most intriguing dialogues with interest for readers of ancient philosophy as well as those who study modern theories of language.

What is the main philosophical gain for a reader of the Cratylus? Led by this question, the author claims that the non-conventialist theory of names developed in the dialogue’s first part is not entirely nullified by the acceptance of conventionalism in the dialogue’s second part. Against some older and some more recent readings, he argues that a core of the non-conventialist theory remains valid in Plato’s view and, together with Plato’s professed conventionalism, represents a complex position on the relation between (...) names and nominata – this is the main outcome of the dialogue (and is also consonant with much of what Plato says in other dialogues). For this reason the paper points out several important distinctions that are made in the first part of the dialogue, notably the introduction of forms of names as a third kind of thing distinct from both names and nominata. It is argued that the forms of names manifest a rational structure behind names, which, in its turn, is the basis for Plato’s semantics and comes forth behind the etymologies and the principle of resemblance as they are successively introduced. (shrink)

Prvi deo ovog rada, objavljen u prethodnom broju casopisa, bio je posvecen razmatranju religijskog porekla dvojnosti 'duha' i 'slova', a zatim i pitanju njenog znacenja u kontekstu filozofije ranog nemackog idealizma. Ovaj, drugi i zakljucni deo rada usredsredjuje se na eticke implikacije tog pitanja, posto je suprotstavljanje 'duha2 Kantovog sistema njegovom 'slovu', uz cesta pozivanja na novozavetno ispunjenje mojsijevskog zakona ljubavlju i verom predstavljalo jednu od osnovnih strategija kriticara Kantove teorije morala. Krajnja konsekvenca ovog pravca kritike Kanta lezi u ukidanju (...) autoriteta transcendentne moralne norme. Ovaj korak, kojim se istovremeno ponistava autoritet teksta kao takvog, a time i stav komentara kao literarnog zanra moze se uociti vec u Hegelovim mladalackim teoloskim spisima, u kojima se zastupa ukidanje transcendencije moralnog zakona njegovim inkorporiranjem u slobodnu subjektivnost koja egzistira u zajednici verujucih hriscana. (shrink)

The purpose of this paper is to shed light on different aspects of the hermeneutical problem in post-Kantian philosophical 'constellation'. In this domain, the problem of the relationship between the text and its commentary is theorized in terms of the antithesis between 'Spirit' and 'Letter', which clearly has religious roots. Therefore, the first part of the paper examines the historical origins of this antithesis, as well as its application in philosophical discussions which developed by the end of the 18th century (...) about the problem of finding the 'true' interpretation to Kant's philosophy. The second part of the text, which is to be published in the next issue of this review, brings the duality of spiritual and literal interpretation into closer connection with the topics of Kant's moral philosophy. Namera ovog rada je da osvetli razlicite aspekte hermeneutickog problema u poslekantovskoj filozofskoj 'konstelaciji'. U ovom podrucju, problem odnosa izmedju teksta i komentara postavlja se u terminima antiteze izmedju 'duha' i 'slova', koja ima prepoznatljive religijske korene. Zato prvi deo rada istrazuje istorijsko poreklo ove antiteze, kao i njenu primenu u filozofskim diskusijama koje su se krajem 18. veka razvile povodom problema pronalazenja 'pravog' tumacenja Kantove filozofije. U drugom delu rada, koji ce biti objavljen u sledecem broju casopisa, dvojnost duhovnog i doslovnog tumacenja dovodi se u uzu vezu sa tematikom Kantove teorije morala. (shrink)

This article analyzes the issues associated with the publication of Martin Heidegger’s Black Notebooks. We attempt to explain the very publication of this document as a kind of experiment the philo...

Name der Zeitschrift: Paragrana Jahrgang: 23 Heft: 2 Seiten: 25-39.

Russian Orthodoxy during the twentieth century presented a rich and varied body of thought about the nature of humanity and the human condition. This article surveys the major thinkers within this tradition, beginning with its background in the Slavophile movement and culminating in the work of more recent Orthodox thinkers such as Sergei Bulgakov, Georges Florovsky, Vladimir Lossky, and Alexander Schmemann.

In this paper we summarise the constraints that low-redshift data—such as supernovae Ia, baryon acoustic oscillations and cosmic chronometers —are able to set on the concordance model and its extensions, as well as on inhomogeneous but isotropic models. We provide a broad overlook into these cosmological scenarios and several aspects of data analysis. In particular, we review a number of systematic issues of SN Ia analysis that include magnitude correction techniques, selection bias and their influence on the inferred cosmological constraints. (...) Furthermore, we examine the isotropic and anisotropic components of the BAO data and their individual relevance for cosmological model-fitting. We extend the discussion presented in earlier works regarding the inferred dynamics of cosmic expansion and its present rate from the low-redshift data. Specifically, we discuss the cosmological constraints on the accelerated expansion and related model-selections. In addition, we extensively talk about the Hubble constant problem, then focus on the low-redshift data constraint on \ that is based on CC. Finally, we present the way in which this result compares to the high-redshift \ estimate and local measurements that are in tension. (shrink)

We consider games over a finite alphabet with Gurevich-Harrington's winning conditions and restraints as in Yakhnis-Yakhnis . The game tree, the Gurevich-Harrington's kernels of the winning condition and the restraints are defined by finite automata. We give an effective criterion to determine the winning player and an effective presentation of a class of finite automata defined winning strategies.Our approach yields an alternative solution to the games considered by Büchi and Landweber . The BL algorithm is an important tool for solving (...) effectively presented games. The differences between the BL and our algorithms are as follows. Our algorithm is uniformly applicable to winning sets that correspond to boolean combinations of BL winning conditions, while the BL algorithm requires a transformation of such boolean combinations into a single BL condition. Our algorithm directly applies to a larger class of game trees for a given game alphabet than does the BL one. We describe Büchi-Landweber's class of winning conditions in a more transparent way by using finite automata and Gurevich-Harrington's form of winning conditions. Our algorithms that determine the winner of the game and find a winning strategy, are based on a translation of the events in the game in terms of the transition table of the automaton representing the game. This automaton differs from the ones that represent BL winning conditions. Both algorithms need further investigation.The algorithm determining the winner in the game, can be used as a verifier of concurrent programs. This is because programs can be viewed as strategies in Gurevich-Harrington's games and program specifications could be regarded as winning conditions for such games. The algorithm which finds a winning strategy could be used as a basis for automated concurrent program design.The present paper is a sequel to Annals of Pure and Applied Logic 48 277–297. (shrink)

This study focuses on determining whether violent contexts influence the perception of aggressiveness in faces analysing spontaneous corrugator supercilii activity. Participants viewed pictures of...

Key premises of the target article by Juslin & Vll (J&V) are challenged. It is also shown that most of the six proposed by the authors as underlying the induction of emotion by music involve nonmusical proximal causes. As a replacement for the state of being-moved is proposed.

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the (...) involved particles is discussed for low energies. (shrink)

This paper examines Gadamer's and Davidson's dialogical models of interpretation. It shows them to be comparable, but importantly dissimilar with respect to the kind of agreement they require for communication to be possible. It is argued that this difference entails different concepts of alterity: they model not only how we talk, but implicitly who we can intelligibly talk to. Another important contribution of this paper is to uncover a distinction in Gadamer between two kinds of agreement missed so far by (...) all commentators. The final section of this paper defends a second thesis, namely that the degree of agreement required by the models is proportional to the conceptual difference it can make intelligible. Hence, the extent of graspable cultural difference is not only an empirical matter, but is entailed by our choice of model. (shrink)